How this instrument works
In a right triangle, the sine of a known angle relates the hypotenuse directly to the leg opposite that angle: multiplying the hypotenuse by the sine of the angle gives that opposite length directly. This page isolates just that one relationship, rather than reporting every measurement a fuller solver would.
This site's Right Triangle Trigonometry calculator already computes that same leg this exact same way, alongside the adjacent one from the same two inputs — this page is a narrower, single-question version for whenever only that one measurement is actually needed, without the extra adjacent figure alongside it.
At the boundary of 90°, the triangle degenerates entirely — the opposite leg grows to match the full hypotenuse, since a 90° angle leaves no adjacent length at all.
- Enter the hypotenuse into the Hypotenuse field.
- Enter the known angle into the Angle field.
- Read Opposite side: the hypotenuse multiplied by the sine of the angle.
- Try an angle of 90° to see the opposite side grow to match the full hypotenuse.
Worked example — hypotenuse 10, angle 30°
A right triangle with hypotenuse 10 and a known 30° angle has an opposite length of 10×sin(30°)=5 — read directly, with no other measurement computed alongside it.
At a 90° angle, that opposite length equals the full hypotenuse, 10 — the triangle has degenerated to a flat line. A hypotenuse of 8 at 45° gives an opposite length of 8×sin(45°)≈5.657.
Questions
What is the relationship between sine, the hypotenuse, and the opposite side?
Sine of a known angle equals the opposite length divided by the hypotenuse — rearranged, that opposite length is simply the hypotenuse multiplied by the sine of the angle.
How is this different from the Right Triangle Trigonometry calculator on this site?
That page computes both the opposite AND the adjacent measurement from the same hypotenuse-and-angle inputs; this page reports just that first one alone, a narrower convenience version for when it's the only figure needed.
What happens to the opposite length as the angle approaches 90°?
It grows to match the full hypotenuse — at exactly 90°, the triangle has flattened entirely, leaving no adjacent length and making the two measurements equal.
What happens to the opposite length as the angle approaches 0°?
It shrinks toward 0 — a vanishingly small angle leaves almost no vertical rise at all relative to the hypotenuse.
Can this be used to find the hypotenuse instead, given the opposite length?
Yes, by rearranging: divide that opposite length by the sine of the angle instead of multiplying — the identical relationship run in reverse.